I agree with Robin, turn image stabilization off. It can introduce a blur especially from 1/125th sec to about 1/640th. Only use it when at very slow shutter speeds of 1/60th or lower or if using long lenses. Also like others said, try manually focusing and see if that helps. Are you shooting RAW and adding sharpening because you will need to add some sharpening? If you are shooting jpegs check sharpening in picture control settings. Good luck, I believe you can get much sharper images from the setup you have.

Your suggestion above is confusing to me. Are you saying 1/125~1/640th are OK for tele's or not? If so then why would they not introduce the same characteristic problems as you suggest for other FL's? I have shot my 70~200 from a kayak with VR and with great results that were in that range.

Also why do you say up to 1/640? Do the problems go away at shutter speeds above that and if so why?